Six workstreams at the derivation bench

Optimization Model Design

The model is the mathematical contract between your business rules and the decision you want to make. We sit with the team that knows the floor and write down every hard limit: capacity per asset, labour ceilings, due dates, dwell windows, zone rules and risk appetite. From that list we derive an objective and a set of constraints that stay readable for years, not months.

We choose the solver family that matches the structure. Pure integer problems get branch and cut. Convex relaxations get continuous methods with fast warm starts. Whatever the class, the model ships with clear assumptions and a documented boundary for when it should be retired and re-derived. Your own analysts can read the sheet, question an inequality and see exactly what we promised.

Scheduling and Routing Algorithms

Real operations never respect a spreadsheet. Rosters collide with leave, deliveries meet traffic, maintenance queues against demand and one late departure ripples through the afternoon. We build schedulers that fix the schedule you actually run, not a clean model of it. Hard rules are guarded as hard constraints; soft preferences carry a price so the machine can trade them deliberately.

Routing work spans single and multi-depot fleets, time windows, driver hour rules, zone loads and fuel or distance objectives. When a route fails mid-shift, the same engine re-optimises the remaining stops in seconds. Crew scheduling covers shift patterns, skill matrices and pairings so a technician, driver or nurse is never asked to do what the rules forbid.

Data Pipeline Engineering

A beautiful objective is worthless fed by dirty input. We architect ingestion pipelines that collect operational events at the cadence your decisions arrive and turn them into cleansed, joined and versioned tables the solver and the reporting layer share. Source of truth stays in your estate; we bring the disciplines of schema checks, backfills and idempotent reruns.

Reconciliation checks compare pipeline output to your billing or dispatch records. Drift monitors watch for the day the incoming world changes shape, such as a new stop type or a renamed depot, and page a human before the model silently goes stale. We document lineage so a planner can trace any number back to the event that produced it.

Forecasting and Estimation Models

Planning is trying to see through fog before the storm arrives. We estimate the forward load your operation will carry: orders per hour, seats per departure, parts per work order, incidents per week, transit time per corridor. Baselines respect weekday rhythms, seasonality and holiday shocks, then the model learns the exceptions your region actually shows.

Errors are reported as honest bands, not flattering points. A plan built on a tight band with a stated confidence floor behaves differently from one that trusts a single persuasive number. Forecast output serves as the demand layer inside the optimizer, so the schedule you compute is built on the same forecast your planners already trust.

Simulation and Scenario Testing

No launch should be the first time a schedule meets a bad day. We forge thousands of synthetic days built from your historical distributions: sudden demand surges, absent crew, jammed yards, weather closed gates and two trucks down at once. The proposed plan reruns across all of them and we count where it cracks, how deep it cracks and who is left waiting.

Scenario answers show decision makers the cost of their hard rules. Want every delivery inside a two-hour window no matter what the snow does? The simulation prices that guarantee in lost coverage and overtime. When a branch is simply not safe to take, the red feasibility cross marks it clearly so nobody confuses a gamble with a plan.

Production Integration and Tuning

The last fold is the one your team touches every day. We expose each solver behind clean endpoints your apps, wearables and web apps can call, with retries, graceful degrade and honest error codes. Deployment includes monitoring for run time and answer quality so a slow solve, an empty fleet or a silent fallback never hides in the dark.

After launch we tune against real production traffic. Gap targets relax where the floor tolerates them, warm starts cut re-run latency and the model learns the incentives your operation truly rewards. When next quarter changes the rules, we re-derive, re-test against replayed history and ship the revision with the same discipline as the first build.

How a derivation engagement runs

Each project follows the same honest arc so both sides know where they stand. Discovery frames the decision and the constraints. Sheet one derives the draft model. Test week breaks it against real and forged data. Draft review puts the sheet in front of your planners for challenge. Production wiring exposes the running solver. Tuning matures it over live weeks.